Convex Polyhedra

1. Auflage 2005
ISBN: 978-3-540-23158-5
Verlag: Springer-Verlag GmbH

Buch, Englisch, 542 Seiten, Format (B × H): 164 mm x 242 mm, Gewicht: 2100 g

Reihe: Springer Monographs in Mathematics

Convex Polyhedra is one of the classics in geometry. There simply is no other book with so many of the aspects of the theory of 3-dimensional convex polyhedra in a comparable way, and in anywhere near its detail and completeness. It is the definitive source of the classical field of convex polyhedra and contains the available answers to the question of the data uniquely determining a convex polyhedron. This question concerns all data pertinent to a polyhedron, e.g. the lengths of edges, areas of faces, etc. This vital and clearly written book includes the basics of convex polyhedra and collects the most general existence theorems for convex polyhedra that are proved by a new and unified method. It is a wonderful source of ideas for students. The English edition includes numerous comments as well as added material and a comprehensive bibliography by V.A. Zalgaller to bring the work up to date. Moreover, related papers by L.A.Shor and Yu.A.Volkov have been added as supplements to this book.

Zielgruppe

Research

Autoren/Hrsg.

Alexandrov, A. D.

Weitere Mitwirkende

Dairbekov, A.

Dairbekov, N.S.

Kutateladze, S.

Kutateladze, Semën Samsonovich

Sossinsky, A.B.

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik
• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie

Inhaltsverzeichnis

Basic Concepts and Simplest Properties of Convex Polyhedra.- Methods and Results.- Uniqueness of Polyhedra with Prescribed Development.- Existence of Polyhedra with Prescribed Development.- Gluing and Flexing Polyhedra with Boundary.- Congruence Conditions for Polyhedra with Parallel Faces.- Existence Theorems for Polyhedra with Prescribed Face Directions.- Relationship Between the Congruence Condition for Polyhedra with Parallel Faces and Other Problems.- Polyhedra with Vertices on Prescribed Rays.- Infinitesimal Rigidity of Convex Polyhedra with Stationary Development.- Infinitesimal Rigidity Conditions for Polyhedra with Prescribed Face Directions.- Supplements.

Über Autor(innen)

A.D. Alexandrov was awarded the Stalin State Prize in 1942, the Lobachevsky prize in 1952, and the Euler Golden Medal in 1992.